It may help to supply the subject again, in the different possible configurations:

1. It is (the car of) one of his girlfriends.

2. It is one of his girlfriend's (cars). (Cf. "It is one (of the cars) of his girlfriend.")

3. It is one of his girlfriends' (cars). (Cf. "It is one (of the cars) of his girlfriends.")

In my opinion, ex. 3 is the most ambiguous. First, I would argue that dyske's #3 is mistaken in that it understands "one" twice--in other words, he is going for the meaning "It is one of the cars of one of his girlfriends," a meaning which I don't think is strictly permitted by the phrase given. Now, the most sensible way of understanding my ex. 3 is as follow: The car belongs to the group of "his girlfriends." This meaning subsumes both the possibility that the car is owned jointly by his multiple girlfriends (whether all of them or a selected group) and indeed the possibility suggested by dyske's #3 above, i.e., that one of his multiple girlfriends owns the car, but the speaker is for some reason unwilling to specify which one and so ascribes the car more generally to the group. Likewise, any combination of girlfriends owning cars is possible: the girlfriends may each own one car, but some or all may own several each, and some or all may own none--so long as there is own car to ascribe to the whole group. Finally, I would caution against using the plural possessor (girlfriends') to signify many cars owned by one girlfriend--the transferal of plural number from the elided subject (here "cars") to its genitive modifier (here "girlfriend's") is a not uncommon mistake make on the basis of specious convenience.

4. A fourth possibility, though even harder to bear than the polygamous exx. 1 and 3, is that the speaker is simply saying "It is one of his girlfriends," i.e., that the CAR ITSELF is the girlfriend of the man in question (which doesn't altogether ignore the question "Whose?" since it does contain a note of the concept of possession). This would obviously involve a metaphorical use of "girlfriend."

While, technically, the answer is ambiguous, I think that Dyske's choice #1 (he has many girlfriends, and the car belongs to one of them) is the one that makes the most sense. If he only had one girlfriend, then the answer would have been "It's his girlfriend's." I think this would be true even if the girlfriend had more than one car. The original question is about who actually owns it, not how many cars they have. How many cars the girlfriend might have and which one it is is irrelevant to the question asked. If "...one...", meant "...one of her cars...", then it would be superfluous information.

Also Karl, perhaps I'm misunderstanding something, but what does "If it were just...it might be easier to interpret this sentence." mean in your original post? You said this was heard in the park. Spoken. All three are usually pronounced the same, so what would make you think there were no apostrophes?

The sentence as I heard it and the reason it struck me as being unusual, phonetically transcribed, was: Whose car is it?It is one of his GIRLZFRENDZ. Though this is a linguistic innovation, to me it conveyed a rather precise information, namely that there are several girlfriends and the car belongs to one of them. The speaker knew the young man, his friend well enough to know that he had several girlfriends but he did not know to which one the car belonged.I wanted to contrast this with the standard English, which as spoken cannot be precisely understood.It is one of his girlfriends'. Or: It is one of his girlfriend's.

It would seem to me that, since the original question is one trying to ascertain ownership, the provided answer must be a person.

"One of his girlfriend's" is more of a quality of the car that hasn't been asked—this is one of many she owns. But that does not designate a person The question asked only contemplates the one car. This answer more answers the question "What is so special about this car?"

One of his girlfriends would answer "Who is she to him?" or "Who is this, then?"

The answer, "one of his girlfriends’ " is the meaning, because that is the only answer that actually answers the question that was asked. It is the only answer that names a person (though which person is not very firmly nailed down, to be sure...).

Now, wait a minute. You said "...one of his GIRLZFRENDZ..." Is this a typo or is the extra Z the "linguistic innovation" you are describing? Did you actually hear "...one of his girlZZZZZfrendZZZZ? Two Z sounds? If so, then this changes everything. This could only mean "It is one of his girl's friends', " meaning that the car belongs to one of the friends of his "girl" (girl, meaning his girlfriend, colloquially). Then again, I suppose it's also possible that you're suggesting that it's some sort of new text-message-esque teen-speak shorthand for something, considering your alternate spelling, what with Z's, missing I's, and all.